Mesh Deformer Modifier - Low poly mesh with softbody simulation deforming a high poly mesh
Parenting only effects the origin and the transforms of the object, never the mesh. There are two ways to achieve this however. 
1. Lattice: you can use a lattice modifier, which can be given a softbody component
2. More practical: Mesh deform modifier. It's a bit cumbersome to set it up, but I'm sure you'll find help with that online.